The 23-year-old, who also spent the 2016-17 campaign on loan at Craven Cottage, suffered the blow in the 35th minute of the team's goalless draw with Leeds United at Elland Road on Tuesday night.
Conor Shaughnessy's challenge resulted in Piazon breaking his fibula, and now he is likely to return to Chelsea for treatment and recovery.
"We are so disappointed for this situation about Lucas Piazon," Sky Sports News quotes Fulham manager Slavisa Jokanovic as saying. "I believe he broke the fibula or broke the leg.
"It's a very bad injury and we will lose him for a long time. It's not a question about complaining - it can be bad luck or a tackle outside of the normal.
"But I'm really disappointed with what I heard from one of the referees who explained 'this is English football and this is completely legal'. I am a 48-year-old man and I've never heard an ugly answer like I heard today in this stadium."
Piazon made 30 appearances in the Championship last season, scoring five goals and creating four assists.